Well, I have seen that as well, but as far as frequency conversion in
a receiver is concerned, I don't think the 6CS6 is a better choice than
the 6BE6. The 6CS6 is optimized as a gated amplifier for extracting
sync signals in TV sets. On the other hand, wa2ise does have a site
that describes the use of a 6BA7 to improve the conversion gain of
a receiver, but that involves some work as the 6BA7 is a bigger, 9-pin
tube.

http://www.geocities.com/wa2ise/radios/12ba7.html#12ba7

The link above describes a 12BA7 to replace a 12BE6 in a table radio
with series-string heaters, but the same idea applies to replacing
a 6BE6 with a 6BA7, although I must admit I have yet to try all this.
Have fun!